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Terdapat fungsi begin mathsize 14px style h left parenthesis x right parenthesis equals f left parenthesis x right parenthesis times g left parenthesis x right parenthesis end style, dan begin mathsize 14px style g left parenthesis x right parenthesis end style adalah hasil dari begin mathsize 14px style f left parenthesis x right parenthesis end style dibagi begin mathsize 14px style 4 x plus 3 end style. Selain itu, diketahui bahwa undefined dibagi begin mathsize 14px style left parenthesis x plus 1 right parenthesis end style bersisa begin mathsize 14px style 1 end style, dan undefined dibagi begin mathsize 14px style left parenthesis x minus 1 right parenthesis end style bersisa begin mathsize 14px style 21 end style. Jika fungsi undefined merupakan fungsi kuadrat, maka fungsi begin mathsize 14px style h left parenthesis x right parenthesis equals end style ...

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style h left parenthesis x right parenthesis equals 16 x cubed plus 28 x squared plus 16 x plus 3 end style.

Pembahasan

Misalkan suku banyak begin mathsize 14px style f left parenthesis x right parenthesis equals a x squared plus b x plus c end style. Jika nilai begin mathsize 14px style x end style diganti begin mathsize 14px style k end style, maka nilai suku banyak undefined untuk begin mathsize 14px style x equals k end style adalah begin mathsize 14px style f left parenthesis k right parenthesis equals a k squared plus b k plus c end style.

Untuk undefined dibagi begin mathsize 14px style left parenthesis x plus 1 right parenthesis end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 1 end cell equals 0 row x equals cell negative 1 end cell end table end style

Substitusikan nilai begin mathsize 14px style x equals negative 1 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 1 right parenthesis end cell equals 1 row cell a minus b plus c end cell equals cell 1 space... space left parenthesis straight i right parenthesis end cell end table end style  

Untuk  undefined dibagi begin mathsize 14px style left parenthesis x minus 1 right parenthesis end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 1 end cell equals 0 row x equals 1 end table end style

Substitusikan nilai begin mathsize 14px style x equals 1 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 1 right parenthesis end cell equals 21 row cell a plus b plus c end cell equals cell 21 space... space left parenthesis ii right parenthesis end cell end table end style 

Eliminasi persamaan (i) dan (ii)

begin mathsize 14px style a minus b plus c equals 1 bottom enclose a plus b plus c equals 21 end enclose space minus space space space space space space minus 2 b equals negative 20 space space space space space space space space space space space space b equals 10 end style

Substitusikan begin mathsize 14px style b equals 10 end style ke persamaan (i)

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a minus b plus c end cell equals 1 row cell a minus 10 plus c end cell equals 1 row cell a plus c end cell equals cell 11 space... space left parenthesis iii right parenthesis end cell end table end style 

Untuk begin mathsize 14px style f left parenthesis x right parenthesis end style dibagi begin mathsize 14px style 4 x plus 3 end style dan diasumsikan sisanya begin mathsize 14px style 0 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 x plus 3 end cell equals 0 row cell 4 x end cell equals cell negative 3 end cell row x equals cell negative 3 over 4 end cell end table end style

Substitusikan nilai begin mathsize 14px style x equals negative 3 over 4 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses negative 3 over 4 close parentheses end cell equals 0 row cell open parentheses negative 3 over 4 close parentheses squared a plus open parentheses negative 3 over 4 close parentheses b plus c end cell equals 0 row cell open parentheses 9 over 16 close parentheses a plus open parentheses negative 3 over 4 close parentheses b plus c end cell equals 0 row cell 9 a minus 12 b plus 16 c end cell equals cell 0 space... space left parenthesis iv right parenthesis end cell row blank blank blank end table end style

Substitusikan begin mathsize 14px style b equals 10 end style ke persamaan  (iv)

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 9 a minus 12 b plus 16 c end cell equals 0 row cell 9 a minus 12 left parenthesis 10 right parenthesis plus 16 c end cell equals 0 row cell 9 a minus 120 plus 16 c end cell equals 0 row cell 9 a plus 16 c end cell equals cell 120 space... space left parenthesis straight v right parenthesis end cell end table end style

Eliminasi persamaan (iii) dan (v)

begin mathsize 14px style space space space space space space a plus c equals 11 space space space space left enclose cross times 9 end enclose space space 9 a plus 9 c equals 99 bottom enclose 9 a plus 16 c equals 120 end enclose space minus space space space space space space space minus 7 c equals negative 21 space space space space space space space space space space space space c equals 3 end style

Substitusikan nilai begin mathsize 14px style c equals 3 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a plus c end cell equals 11 row cell a plus 3 end cell equals 11 row a equals 8 end table end style

Sehingga, diperoleh fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style adalah begin mathsize 14px style f left parenthesis x right parenthesis equals 8 x squared plus 10 x plus 3 end style.

undefined 

Maka, nilai begin mathsize 14px style g left parenthesis x right parenthesis equals 8 x plus 4 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell f left parenthesis x right parenthesis times g left parenthesis x right parenthesis end cell row blank equals cell open parentheses 8 x squared plus 10 x plus 3 close parentheses times left parenthesis 8 x plus 4 right parenthesis end cell row blank equals cell 64 x cubed plus 32 x squared plus 80 x squared plus 40 x plus 24 x plus 12 end cell row blank equals cell 64 x cubed plus 112 x squared plus 64 x plus 12 end cell row blank equals cell 16 x cubed plus 28 x squared plus 16 x plus 3 end cell end table end style

Jadi, begin mathsize 14px style h left parenthesis x right parenthesis equals 16 x cubed plus 28 x squared plus 16 x plus 3 end style.

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